In this work the position, velocity and acceleration analyses of a four-degrees-of-freedom serial manipulator are approached mainly by means of the theory of screws. Closed-form solutions are easily obtained for the displacement analysis of the mechanism owing the decoupled action of the generalized coordinates, while the input-output equations of velocity and acceleration of the manipulator are systematically obtained by means of the theory of screws. A case study is included with the purpose to exemplify the application of the method.